Question: What do the following two equations represent? $3x+2y = -1$ $-3x-2y = 4$
Answer: Putting the first equation in $y = mx + b$ form gives: $3x+2y = -1$ $2y = -3x-1$ $y = -\dfrac{3}{2}x - \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $-3x-2y = 4$ $-2y = 3x+4$ $y = -\dfrac{3}{2}x - 2$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.